A novel side-chain orientation dependent potential derived from random-walk reference state for protein fold selection and structure prediction

A simple neural network implementation of generalized solvation free energy for assessment of protein structural models

Rapid and accurate assessment of protein structural models is essential for protein structure prediction and design. Great progress has been made in this regard, especially by recent application of "knowledge-based" potentials. Various machine learning based protein structural model quality assessment methods are also quite successful. However, performance of traditional "physics-based" models has not been as effective. Based on our analysis of the fundamental computational limitation behind unsatisfactory performance of "physics-based" models, we propose a generalized solvation free energy (GSFE) framework, which is intrinsically flexible for multi-scale treatments and is amenable for machine learning implementation. Finally, we implemented a simple example of backbone-based residue level GSFE with neural network, which was found to have competitive performance when compared with highly complex latest "knowledge-based" atomic potentials in distinguishing native structures from decoys.

Unsupervised and Supervised Learning over theEnergy Landscape for Protein Decoy Selection

The energy landscape that organizes microstates of a molecular system and governs theunderlying molecular dynamics exposes the relationship between molecular form/structure, changesto form, and biological activity or function in the cell. However, several challenges stand in the wayof leveraging energy landscapes for relating structure and structural dynamics to function. Energylandscapes are high-dimensional, multi-modal, and often overly-rugged. Deep wells or basins inthem do not always correspond to stable structural states but are instead the result of inherentinaccuracies in semi-empirical molecular energy functions. Due to these challenges, energeticsis typically ignored in computational approaches addressing long-standing central questions incomputational biology, such as protein decoy selection. In the latter, the goal is to determine over apossibly large number of computationally-generated three-dimensional structures of a protein thosestructures that are biologically-active/native. In recent work, we have recast our attention on theprotein energy landscape and its role in helping us to advance decoy selection. Here, we summarizesome of our successes so far in this direction via unsupervised learning. More importantly, we furtheradvance the argument that the energy landscape holds valuable information to aid and advance thestate of protein decoy selection via novel machine learning methodologies that leverage supervisedlearning. Our focus in this article is on decoy selection for the purpose of a rigorous, quantitativeevaluation of how leveraging protein energy landscapes advances an important problem in proteinmodeling. However, the ideas and concepts presented here are generally useful to make discoveriesin studies aiming to relate molecular structure and structural dynamics to function.

Protein model accuracy estimation based on local structure quality assessment using 3D convolutional neural network

In protein tertiary structure prediction, model quality assessment programs (MQAPs) are often used to select the final structural models from a pool of candidate models generated by multiple templates and prediction methods. The 3-dimensional convolutional neural network (3DCNN) is an expansion of the 2DCNN and has been applied in several fields, including object recognition. The 3DCNN is also used for MQA tasks, but the performance is low due to several technical limitations related to protein tertiary structures, such as orientation alignment. We proposed a novel single-model MQA method based on local structure quality evaluation using a deep neural network containing 3DCNN layers. The proposed method first assesses the quality of local structures for each residue and then evaluates the quality of whole structures by integrating estimated local qualities. We analyzed the model using the CASP11, CASP12, and 3D-Robot datasets and compared the performance of the model with that of the previous 3DCNN method based on whole protein structures. The proposed method showed a significant improvement compared to the previous 3DCNN method for multiple evaluation measures. We also compared the proposed method to other state-of-the-art methods. Our method showed better performance than the previous 3DCNN-based method and comparable accuracy as the current best single-model methods; particularly, in CASP11 stage2, our method showed a Pearson coefficient of 0.486, which was better than those of the best single-model methods (0.366–0.405). A standalone version of the proposed method and data files are available at https://github.com/ishidalab-titech/3DCNN_MQA.

Purely Structural Protein Scoring Functions Using Support Vector Machine and Ensemble Learning

The function of a protein is determined by its structure, which creates a need for efficient methods of protein structure determination to advance scientific and medical research. Because current experimental structure determination methods carry a high price tag, computational predictions are highly desirable. Given a protein sequence, computational methods produce numerous 3D structures known as decoys. Selection of the best quality decoys is both challenging and essential as the end users can handle only a few ones. Therefore, scoring functions are central to decoy selection. They combine measurable features into a single number indicator of decoy quality. Unfortunately, current scoring functions do not consistently select the best decoys. Machine learning techniques offer great potential to improve decoy scoring. This paper presents two machine-learning based scoring functions to predict the quality of proteins structures, i.e., the similarity between the predicted structure and the experimental one without knowing the latter. We use different metrics to compare these scoring functions against three state-of-the-art scores. This is a first attempt at comparing different scoring functions using the same non-redundant dataset for training and testing and the same features. The results show that adding informative features may be more significant than the method used.

Wnt Binding Affinity Prediction for Putative Frizzled-Type Cysteine-Rich Domains

Several proteins other than the frizzled receptors (Fzd) and the secreted Frizzled-related proteins (sFRP) contain Fzd-type cysteine-rich domains (CRD). We have termed these domains “putative Fzd-type CRDs”, as the relevance of Wnt signalling in the majority of these is unknown; the RORs, an exception to this, are well known for mediating non-canonical Wnt signalling. In this study, we have predicted the likely binding affinity of all Wnts for all putative Fzd-type CRDs. We applied both our previously determined Wnt‒Fzd CRD binding affinity prediction model, as well as a newly devised model wherein the lipid term was forced to contribute favourably to the predicted binding energy. The results obtained from our new model indicate that certain putative Fzd CRDs are much more likely to bind Wnts, in some cases exhibiting selectivity for specific Wnts. The results of this study inform the investigation of Wnt signalling modulation beyond Fzds and sFRPs.

OPUS-Rota2: An Improved Fast and Accurate Side-Chain Modeling Method

Side-chain modeling plays a critical role in protein structure prediction. However, in many current methods, balancing the speed and accuracy is still challenging. In this paper, on the basis of our previous work OPUS-Rota (Protein Sci. 2008, 17, 1576-1585), we introduce a new side-chain modeling method, OPUS-Rota2, which is tested on both a 65-protein test set (DB65) in the OPUS-Rota paper and a 379-protein test set (DB379) in the SCWRL4 paper. If the main chain is native, OPUS-Rota2 is more accurate than OPUS-Rota, SCWRL4, and OSCAR-star but slightly less accurate than OSCAR-o. Also, if the main chain is non-native, OPUS-Rota2 is more accurate than any other method. Moreover, OPUS-Rota2 is significantly faster than any other method, in particular, 2 orders of magnitude faster than OSCAR-o. Thus, the combination of higher accuracy and speed of OPUS-Rota2 in modeling side chains on both the native and non-native main chains makes OPUS-Rota2 a very useful tool in protein structure modeling.

Estimation of model accuracy in CASP13

Methods to reliably estimate the accuracy of 3D models of proteins are both a fundamental part of most protein folding pipelines and important for reliable identification of the best models when multiple pipelines are used. Here, we describe the progress made from CASP12 to CASP13 in the field of estimation of model accuracy (EMA) as seen from the progress of the most successful methods in CASP13. We show small but clear progress, that is, several methods perform better than the best methods from CASP12 when tested on CASP13 EMA targets. Some progress is driven by applying deep learning and residue-residue contacts to model accuracy prediction. We show that the best EMA methods select better models than the best servers in CASP13, but that there exists a great potential to improve this further. Also, according to the evaluation criteria based on local similarities, such as lDDT and CAD, it is now clear that single model accuracy methods perform relatively better than consensus-based methods.

Artificial intelligence-based multi-objective optimization protocol for protein structure refinement

MOTIVATION

Protein structure refinement is an important step of protein structure prediction. Existing approaches have generally used a single scoring function combined with Monte Carlo method or Molecular Dynamics algorithm. The one-dimension optimization of a single energy function may take the structure too far away without a constraint. The basic motivation of our study is to reduce the bias problem caused by minimizing only a single energy function due to the very diversity of different protein structures.

RESULTS

We report a new Artificial Intelligence-based protein structure Refinement method called AIR. Its fundamental idea is to use multiple energy functions as multi-objectives in an effort to correct the potential inaccuracy from a single function. A multi-objective particle swarm optimization algorithm-based structure refinement is designed, where each structure is considered as a particle in the protocol. With the refinement iterations, the particles move around. The quality of particles in each iteration is evaluated by three energy functions, and the non-dominated particles are put into a set called Pareto set. After enough iteration times, particles from the Pareto set are screened and part of the top solutions are outputted as the final refined structures. The multi-objective energy function optimization strategy designed in the AIR protocol provides a different constraint view of the structure, by extending the one-dimension optimization to a new three-dimension space optimization driven by the multi-objective particle swarm optimization engine. Experimental results on CASP11, CASP12 refinement targets and blind tests in CASP 13 turn to be promising.

AVAILABILITY AND IMPLEMENTATION

The AIR is available online at: www.csbio.sjtu.edu.cn/bioinf/AIR/.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

What is the best reference state for building statistical potentials in RNA 3D structure evaluation?

Knowledge-based statistical potentials have been shown to be efficient in protein structure evaluation/prediction, and the core difference between various statistical potentials is attributed to the choice of reference states. However, for RNA 3D structure evaluation, a comprehensive examination on reference states is still lacking. In this work, we built six statistical potentials based on six reference states widely used in protein structure evaluation, including averaging, quasi-chemical approximation, atom-shuffled, finite-ideal-gas, spherical-noninteracting, and random-walk-chain reference states, and we examined the six reference states against three RNA test sets including six subsets. Our extensive examinations show that, overall, for identifying native structures and ranking decoy structures, the finite-ideal-gas and random-walk-chain reference states are slightly superior to others, while for identifying near-native structures, there is only a slight difference between these reference states. Our further analyses show that the performance of a statistical potential is apparently dependent on the quality of the training set. Furthermore, we found that the performance of a statistical potential is closely related to the origin of test sets, and for the three realistic test subsets, the six statistical potentials have overall unsatisfactory performance. This work presents a comprehensive examination on the existing reference states and statistical potentials for RNA 3D structure evaluation.

Sequence Tolerance of a Single-Domain Antibody with a High Thermal Stability: Comparison of Computational and Experimental Fitness Profiles

The sequence fitness of a llama single-domain antibody with an unusually high thermal stability is explored by a combined computational and experimental study. Starting with the X-ray crystallographic structure, RosettaBackrub simulations were applied to model sequence-structure tolerance profiles and identify key substitution sites. From the model calculations, an experimental site-directed mutagenesis was used to produce a panel of mutants, and their melting temperatures were determined by thermal denaturation. The results reveal a sequence fitness of an excess stability of approximately 12 °C, a value taken from a decrease in the melting temperature of an electrostatic charge-reversal substitution in the CRD3 without a deleterious effect on the binding affinity to the antigen. The tolerance for the disruption of antigen recognition without loss in the thermal stability was demonstrated by the introduction of a proline in place of a tyrosine in the CDR2, producing a mutant that eliminated binding. To further assist the sequence design and the selection of engineered single-domain antibodies, an assessment of different computational strategies is provided of their accuracy in the detection of substitution "hot spots" in the sequence tolerance landscape.

Driven to near-experimental accuracy by refinement via molecular dynamics simulations

Protein model refinement has been an essential part of successful protein structure prediction. Molecular dynamics simulation-based refinement methods have shown consistent improvement of protein models. There had been progress in the extent of refinement for a few years since the idea of ensemble averaging of sampled conformations emerged. There was little progress in CASP12 because conformational sampling was not sufficiently diverse due to harmonic restraints. During CASP13, a new refinement method was tested that achieved significant improvements over CASP12. The new method intended to address previous bottlenecks in the refinement problem by introducing new features. Flat-bottom harmonic restraints replaced harmonic restraints, sampling was performed iteratively, and a new scoring function and selection criteria were used. The new protocol expanded conformational sampling at reduced computational costs. In addition to overall improvements, some models were refined significantly to near-experimental accuracy.

ANDIS: an atomic angle- and distance-dependent statistical potential for protein structure quality assessment

Background

The knowledge-based statistical potential has been widely used in protein structure modeling and model quality assessment. They are commonly evaluated based on their abilities of native recognition as well as decoy discrimination. However, these two aspects are found to be mutually exclusive in many statistical potentials.

Results

We developed an atomic ANgle- and DIStance-dependent (ANDIS) statistical potential for protein structure quality assessment with distance cutoff being a tunable parameter. When distance cutoff is ≤9.0 Å, “effective atomic interaction” is employed to enhance the ability of native recognition. For a distance cutoff of ≥10 Å, the distance-dependent atom-pair potential with random-walk reference state is combined to strengthen the ability of decoy discrimination. Benchmark tests on 632 structural decoy sets from diverse sources demonstrate that ANDIS outperforms other state-of-the-art potentials in both native recognition and decoy discrimination.

Conclusions

Distance cutoff is a crucial parameter for distance-dependent statistical potentials. A lower distance cutoff is better for native recognition, while a higher one is favorable for decoy discrimination. The ANDIS potential is freely available as a standalone application at http://qbp.hzau.edu.cn/ANDIS/.

Electronic supplementary material

The online version of this article (10.1186/s12859-019-2898-y) contains supplementary material, which is available to authorized users.

Methods for the Refinement of Protein Structure 3D Models

The refinement of predicted 3D protein models is crucial in bringing them closer towards experimental accuracy for further computational studies. Refinement approaches can be divided into two main stages: The sampling and scoring stages. Sampling strategies, such as the popular Molecular Dynamics (MD)-based protocols, aim to generate improved 3D models. However, generating 3D models that are closer to the native structure than the initial model remains challenging, as structural deviations from the native basin can be encountered due to force-field inaccuracies. Therefore, different restraint strategies have been applied in order to avoid deviations away from the native structure. For example, the accurate prediction of local errors and/or contacts in the initial models can be used to guide restraints. MD-based protocols, using physics-based force fields and smart restraints, have made significant progress towards a more consistent refinement of 3D models. The scoring stage, including energy functions and Model Quality Assessment Programs (MQAPs) are also used to discriminate near-native conformations from non-native conformations. Nevertheless, there are often very small differences among generated 3D models in refinement pipelines, which makes model discrimination and selection problematic. For this reason, the identification of the most native-like conformations remains a major challenge.

Protein tertiary structure modeling driven by deep learning and contact distance prediction in CASP13

Predicting residue‐residue distance relationships (eg, contacts) has become the key direction to advance protein structure prediction since 2014 CASP11 experiment, while deep learning has revolutionized the technology for contact and distance distribution prediction since its debut in 2012 CASP10 experiment. During 2018 CASP13 experiment, we enhanced our MULTICOM protein structure prediction system with three major components: contact distance prediction based on deep convolutional neural networks, distance‐driven template‐free (ab initio) modeling, and protein model ranking empowered by deep learning and contact prediction. Our experiment demonstrates that contact distance prediction and deep learning methods are the key reasons that MULTICOM was ranked 3rd out of all 98 predictors in both template‐free and template‐based structure modeling in CASP13. Deep convolutional neural network can utilize global information in pairwise residue‐residue features such as coevolution scores to substantially improve contact distance prediction, which played a decisive role in correctly folding some free modeling and hard template‐based modeling targets. Deep learning also successfully integrated one‐dimensional structural features, two‐dimensional contact information, and three‐dimensional structural quality scores to improve protein model quality assessment, where the contact prediction was demonstrated to consistently enhance ranking of protein models for the first time. The success of MULTICOM system clearly shows that protein contact distance prediction and model selection driven by deep learning holds the key of solving protein structure prediction problem. However, there are still challenges in accurately predicting protein contact distance when there are few homologous sequences, folding proteins from noisy contact distances, and ranking models of hard targets.

Forging tools for refining predicted protein structures

Refining predicted protein structures with all-atom molecular dynamics simulations is one route to producing, entirely by computational means, structural models of proteins that rival in quality those that are determined by X-ray diffraction experiments. Slow rearrangements within the compact folded state, however, make routine refinement of predicted structures by unrestrained simulations infeasible. In this work, we draw inspiration from the fields of metallurgy and blacksmithing, where practitioners have worked out practical means of controlling equilibration by mechanically deforming their samples. We describe a two-step refinement procedure that involves identifying collective variables for mechanical deformations using a coarse-grained model and then sampling along these deformation modes in all-atom simulations. Identifying those low-frequency collective modes that change the contact map the most proves to be an effective strategy for choosing which deformations to use for sampling. The method is tested on 20 refinement targets from the CASP12 competition and is found to induce large structural rearrangements that drive the structures closer to the experimentally determined structures during relatively short all-atom simulations of 50 ns. By examining the accuracy of side-chain rotamer states in subensembles of structures that have varying degrees of similarity to the experimental structure, we identified the reorientation of aromatic side chains as a step that remains slow even when encouraging global mechanical deformations in the all-atom simulations. Reducing the side-chain rotamer isomerization barriers in the all-atom force field is found to further speed up refinement.

OPUS-SSF: A side-chain-inclusive scoring function for ranking protein structural models

We introduce a side-chain-inclusive scoring function, named OPUS-SSF, for ranking protein structural models. The method builds a scoring function based on the native distributions of the coordinate components of certain anchoring points in a local molecular system for peptide segments of 5, 7, 9, and 11 residues in length. Differing from our previous OPUS-CSF [Xu et al., Protein Sci. 2018; 27: 286-292], which exclusively uses main chain information, OPUS-SSF employs anchoring points on side chains so that the effect of side chains is taken into account. The performance of OPUS-SSF was tested on 15 decoy sets containing totally 603 proteins, and 571 of them had their native structures recognized from their decoys. Similar to OPUS-CSF, OPUS-SSF does not employ the Boltzmann formula in constructing scoring functions. The results indicate that OPUS-SSF has achieved a significant improvement on decoy recognition and it should be a very useful tool for protein structural prediction and modeling.

Toward Structure Determination of Disulfide-Rich Peptides Using Chemical Shift-Based Methods

Disulfide-rich peptides are a class of molecules for which NMR spectroscopy has been the primary tool for structural characterization. Here, we explore whether the process can be achieved by using structural information encoded in chemical shifts. We examine (i) a representative set of five cyclic disulfide-rich peptides that have high-resolution NMR and X-ray structures and (ii) a larger set of 100 disulfide-rich peptides from the PDB. Accuracy of the calculated structures was dependent on the methods used for searching through conformational space and for identifying native conformations. Although Hα chemical shifts could be predicted reasonably well using SHIFTX, agreement between predicted and experimental chemical shifts was sufficient for identifying native conformations for only some peptides in the representative set. Combining chemical shift data with the secondary structure information and potential energy calculations improved the ability to identify native conformations. Additional use of sparse distance restraints or homology information to restrict the search space also improved the resolution of the calculated structures. This study demonstrates that abbreviated methods have potential for elucidation of peptide structures to high resolution and further optimization of these methods, e.g., improvement in chemical shift prediction accuracy, will likely help transition these methods into the mainstream of disulfide-rich peptide structural biology.

Protein model quality assessment using 3D oriented convolutional neural networks

Motivation

Protein model quality assessment (QA) is a crucial and yet open problem in structural bioinformatics. The current best methods for single-model QA typically combine results from different approaches, each based on different input features constructed by experts in the field. Then, the prediction model is trained using a machine-learning algorithm. Recently, with the development of convolutional neural networks (CNN), the training paradigm has changed. In computer vision, the expert-developed features have been significantly overpassed by automatically trained convolutional filters. This motivated us to apply a three-dimensional (3D) CNN to the problem of protein model QA.

Results

We developed Ornate (Oriented Routed Neural network with Automatic Typing)—a novel method for single-model QA. Ornate is a residue-wise scoring function that takes as input 3D density maps. It predicts the local (residue-wise) and the global model quality through a deep 3D CNN. Specifically, Ornate aligns the input density map, corresponding to each residue and its neighborhood, with the backbone topology of this residue. This circumvents the problem of ambiguous orientations of the initial models. Also, Ornate includes automatic identification of atom types and dynamic routing of the data in the network. Established benchmarks (CASP 11 and CASP 12) demonstrate the state-of-the-art performance of our approach among single-model QA methods.

Availability and implementation

The method is available at https://team.inria.fr/nano-d/software/Ornate/. It consists of a C++ executable that transforms molecular structures into volumetric density maps, and a Python code based on the TensorFlow framework for applying the Ornate model to these maps.

Supplementary information

Supplementary data are available at Bioinformatics online.

KORP: knowledge-based 6D potential for fast protein and loop modeling

Motivation

Knowledge-based statistical potentials constitute a simpler and easier alternative to physics-based potentials in many applications, including folding, docking and protein modeling. Here, to improve the effectiveness of the current approximations, we attempt to capture the six-dimensional nature of residue–residue interactions from known protein structures using a simple backbone-based representation.

Results

We have developed KORP, a knowledge-based pairwise potential for proteins that depends on the relative position and orientation between residues. Using a minimalist representation of only three backbone atoms per residue, KORP utilizes a six-dimensional joint probability distribution to outperform state-of-the-art statistical potentials for native structure recognition and best model selection in recent critical assessment of protein structure prediction and loop-modeling benchmarks. Compared with the existing methods, our side-chain independent potential has a lower complexity and better efficiency. The superior accuracy and robustness of KORP represent a promising advance for protein modeling and refinement applications that require a fast but highly discriminative energy function.

Availability and implementation

http://chaconlab.org/modeling/korp.

Supplementary information

Supplementary data are available at Bioinformatics online.

An improved protein structure evaluation using a semi-empirically derived structure property

BACKGROUND

In the backdrop of challenge to obtain a protein structure under the known limitations of both experimental and theoretical techniques, the need of a fast as well as accurate protein structure evaluation method still exists to substantially reduce a huge gap between number of known sequences and structures. Among currently practiced theoretical techniques, homology modelling backed by molecular dynamics based optimization appears to be the most popular one. However it suffers from contradictory indications of different validation parameters generated from a set of protein models which are predicted against a particular target protein. For example, in one model Ramachandran Score may be quite high making it acceptable, whereas, its potential energy may not be very low making it unacceptable and vice versa. Towards resolving this problem, the main objective of this study was fixed as to utilize a simple experimentally derived output, Surface Roughness Index of concerned protein of unknown structure as an intervening agent that could be obtained using ordinary microscopic images of heat denatured aggregates of the same protein.

RESULT

It was intriguing to observe that direct experimental knowledge of the concerned protein, however simple it may be, might give insight on acceptability of its particular structural model out of a confusion set of models generated from database driven comparative technique for structure prediction. The result obtained from a widely varying structural class of proteins indicated that speed of protein structure evaluation can be further enhanced without compromising with accuracy by recruiting simple experimental output.

CONCLUSION

In this work, a semi-empirical methodological approach was provided for improving protein structure evaluation. It showed that, once structure models of a protein were obtained through homology technique, the problem of selection of a best model out of a confusion set of Pareto-optimal structures could be resolved by employing a structure agent directly obtainable through experiment with the same protein as experimental ingredient. Overall, in the backdrop of getting a reasonably accurate protein structure of pathogens causing epidemics or biological warfare, such approach could be of use as a plausible solution for fast drug design.

Experimental accuracy in protein structure refinement via molecular dynamics simulations

Refinement is the last step in protein structure prediction pipelines to convert approximate homology models to experimental accuracy. Protocols based on molecular dynamics (MD) simulations have shown promise, but current methods are limited to moderate levels of consistent refinement. To explore the energy landscape between homology models and native structures and analyze the challenges of MD-based refinement, eight test cases were studied via extensive simulations followed by Markov state modeling. In all cases, native states were found very close to the experimental structures and at the lowest free energies, but refinement was hindered by a rough energy landscape. Transitions from the homology model to the native states require the crossing of significant kinetic barriers on at least microsecond time scales. A significant energetic driving force toward the native state was lacking until its immediate vicinity, and there was significant sampling of off-pathway states competing for productive refinement. The role of recent force field improvements is discussed and transition paths are analyzed in detail to inform which key transitions have to be overcome to achieve successful refinement.

Template-Guided Protein Structure Prediction and Refinement Using Optimized Folding Landscape Force Fields

When good structural templates can be identified, template-based modeling is the most reliable way to predict the tertiary structure of proteins. In this study, we combine template-based modeling with a realistic coarse-grained force field, AWSEM, that has been optimized using the principles of energy landscape theory. The Associative memory, Water mediated, Structure and Energy Model (AWSEM) is a coarse-grained force field having both transferable tertiary interactions and knowledge-based local-in-sequence interaction terms. We incorporate template information into AWSEM by introducing soft collective biases to the template structures, resulting in a model that we call AWSEM-Template. Structure prediction tests on eight targets, four of which are in the low sequence identity "twilight zone" of homology modeling, show that AWSEM-Template can achieve high-resolution structure prediction. Our results also confirm that using a combination of AWSEM and a template-guided potential leads to more accurate prediction of protein structures than simply using a template-guided potential alone. Free energy profile analyses demonstrate that the soft collective biases to the template effectively increase funneling toward native-like structures while still allowing significant flexibility so as to allow for correction of discrepancies between the target structure and the template. A further stage of refinement using all-atom molecular dynamics augmented with soft collective biases to the structures predicted by AWSEM-Template leads to a further improvement of both backbone and side-chain accuracy by maintaining sufficient flexibility but at the same time discouraging unproductive unfolding events often seen in unrestrained all-atom refinement simulations. The all-atom refinement simulations also reduce patches of frustration of the initial predictions. Some of the backbones found among the structures produced during the initial coarse-grained prediction step already have CE-RMSD values of less than 3 Å with 90% or more of the residues aligned to the experimentally solved structure for all targets. All-atom structures generated during the following all-atom refinement simulations, which started from coarse-grained structures that were chosen without reference to any knowledge about the native structure, have CE-RMSD values of less than 2.5 Å with 90% or more of the residues aligned for 6 out of 8 targets. Clustering low energy structures generated during the initial coarse-grained annealing picks out reliably structures that are within 1 Å of the best sampled structures in 5 out of 8 cases. After the all-atom refinement, structures that are within 1 Å of the best sampled structures can be selected using a simple algorithm based on energetic features alone in 7 out of 8 cases.

Predicting improved protein conformations with a temporal deep recurrent neural network

Accurate protein structure prediction from amino acid sequence is still an unsolved problem. The most reliable methods centre on template based modelling. However, the accuracy of these models entirely depends on the availability of experimentally resolved homologous template structures. In order to generate more accurate models, extensive physics based molecular dynamics (MD) refinement simulations are performed to sample many different conformations to find improved conformational states. In this study, we propose a deep recurrent network model, called DeepTrajectory, that is able to identify these improved conformational states, with high precision, from a variety of different MD based sampling protocols. The proposed model learns the temporal patterns of features computed from MD trajectory data in order to classify whether each recorded simulation snapshot is an improved quality conformational state, decreased quality conformational state or whether there is no perceivable change in state with respect to the starting conformation. The model was trained and tested on 904 trajectories from 42 different protein systems with a cumulative number of more than 1.7 million snapshots. We show that our model outperforms other state of the art machine-learning algorithms that do not consider temporal dependencies. To our knowledge, DeepTrajectory is the first implementation of a time-dependent deep-learning protocol that is re-trainable and able to adapt to any new MD based sampling procedure, thereby demonstrating how a neural network can be used to learn the latter part of the protein folding funnel.

Role of solvent accessibility for aggregation-prone patches in protein folding

The arrangement of amino acids in a protein sequence encodes its native folding. However, the same arrangement in aggregation-prone regions may cause misfolding as a result of local environmental stress. Under normal physiological conditions, such regions congregate in the protein’s interior to avoid aggregation and attain the native fold. We have used solvent accessibility of aggregation patches (SAAP_p) to determine the packing of aggregation-prone residues. Our results showed that SAAP_p has low values for native crystal structures, consistent with protein folding as a mechanism to minimize the solvent accessibility of aggregation-prone residues. SAAP_p also shows an average correlation of 0.76 with the global distance test (GDT) score on CASP12 template-based protein models. Using SAAP_p scores and five structural features, a random forest machine learning quality assessment tool, SAAP-QA, showed 2.32 average GDT loss between best model predicted and actual best based on GDT score on independent CASP test data, with the ability to discriminate native-like folds having an AUC of 0.94. Overall, the Pearson correlation coefficient (PCC) between true and predicted GDT scores on independent CASP data was 0.86 while on the external CAMEO dataset, comprising high quality protein structures, PCC and average GDT loss were 0.71 and 4.46 respectively. SAAP-QA can be used to detect the quality of models and iteratively improve them to native or near-native structures.

Improving low-accuracy protein structures using enhanced sampling techniques

In this paper, we report results of using enhanced sampling and blind selection techniques for high-accuracy protein structural refinement. By combining a parallel continuous simulated tempering (PCST) method, previously developed by Zang et al. [J. Chem. Phys. 141, 044113 (2014)], and the structure based model (SBM) as restraints, we refined 23 targets (18 from the refinement category of the CASP10 and 5 from that of CASP12). We also designed a novel model selection method to blindly select high-quality models from very long simulation trajectories. The combined use of PCST-SBM with the blind selection method yielded final models that are better than initial models. For Top-1 group, 7 out of 23 targets had better models (greater global distance test total scores) than the critical assessment of structure prediction participants. For Top-5 group, 10 out of 23 were better. Our results justify the crucial position of enhanced sampling in protein structure prediction and refinement and demonstrate that a considerable improvement of low-accuracy structures is achievable with current force fields.

Contact Potential for Structure Prediction of Proteins and Protein Complexes from Potts Model

The energy function is the key component of protein modeling methodology. This work presents a semianalytical approach to the development of contact potentials for protein structure modeling. Residue-residue and atom-atom contact energies were derived by maximizing the probability of observing native sequences in a nonredundant set of protein structures. The optimization task was formulated as an inverse statistical mechanics problem applied to the Potts model. Its solution by pseudolikelihood maximization provides consistent estimates of coupling constants at atomic and residue levels. The best performance was achieved when interacting atoms were grouped according to their physicochemical properties. For individual protein structures, the performance of the contact potentials in distinguishing near-native structures from the decoys is similar to the top-performing scoring functions. The potentials also yielded significant improvement in the protein docking success rates. The potentials recapitulated experimentally determined protein stability changes upon point mutations and protein-protein binding affinities. The approach offers a different perspective on knowledge-based potentials and may serve as the basis for their further development.

Structure refinement of membrane proteins via molecular dynamics simulations

A refinement protocol based on physics-based techniques established for water soluble proteins is tested for membrane protein structures. Initial structures were generated by homology modeling and sampled via molecular dynamics simulations in explicit lipid bilayer and aqueous solvent systems. Snapshots from the simulations were selected based on scoring with either knowledge-based or implicit membrane-based scoring functions and averaged to obtain refined models. The protocol resulted in consistent and significant refinement of the membrane protein structures similar to the performance of refinement methods for soluble proteins. Refinement success was similar between sampling in the presence of lipid bilayers and aqueous solvent but the presence of lipid bilayers may benefit the improvement of lipid-facing residues. Scoring with knowledge-based functions (DFIRE and RWplus) was found to be as good as scoring using implicit membrane-based scoring functions suggesting that differences in internal packing is more important than orientations relative to the membrane during the refinement of membrane protein homology models.

Contact prediction is hardest for the most informative contacts, but improves with the incorporation of contact potentials

Co-evolution between pairs of residues in a multiple sequence alignment (MSA) of homologous proteins has long been proposed as an indicator of structural contacts. Recently, several methods, such as direct-coupling analysis (DCA) and MetaPSICOV, have been shown to achieve impressive rates of contact prediction by taking advantage of considerable sequence data. In this paper, we show that prediction success rates are highly sensitive to the structural definition of a contact, with more permissive definitions (i.e., those classifying more pairs as true contacts) naturally leading to higher positive predictive rates, but at the expense of the amount of structural information contributed by each contact. Thus, the remaining limitations of contact prediction algorithms are most noticeable in conjunction with geometrically restrictive contacts—precisely those that contribute more information in structure prediction. We suggest that to improve prediction rates for such “informative” contacts one could combine co-evolution scores with additional indicators of contact likelihood. Specifically, we find that when a pair of co-varying positions in an MSA is occupied by residue pairs with favorable statistical contact energies, that pair is more likely to represent a true contact. We show that combining a contact potential metric with DCA or MetaPSICOV performs considerably better than DCA or MetaPSICOV alone, respectively. This is true regardless of contact definition, but especially true for stricter and more informative contact definitions. In summary, this work outlines some remaining challenges to be addressed in contact prediction and proposes and validates a promising direction towards improvement.

A Comprehensive Analysis of Anion-Quadrupole Interactions in Protein Structures

The edgewise interactions of anions with phenylalanine (Phe) aromatic rings in proteins, known as anion-quadrupole interactions, have been well studied. However, the anion-quadrupole interactions of the tyrosine (Tyr) and tryptophan (Trp) rings have been less well studied, probably because these have been considered weaker than interactions of anions hydrogen bonded to Trp/Tyr side chains. Distinguishing such hydrogen bonding interactions, we comprehensively surveyed the edgewise interactions of certain anions (aspartate, glutamate, and phosphate) with Trp, Tyr, and Phe rings in high-resolution, nonredundant protein single chains and interfaces (protein-protein, DNA/RNA-protein, and membrane-protein). Trp/Tyr anion-quadrupole interactions are common, with Trp showing the highest propensity and average interaction energy for this type of interaction. The energy of an anion-quadrupole interaction (-15.0 to 0.0 kcal/mol, based on quantum mechanical calculations) depends not only on the interaction geometry but also on the ring atom. The phosphate anions at DNA/RNA-protein interfaces interact with aromatic residues with energies comparable to that of aspartate/glutamate anion-quadrupole interactions. At DNA-protein interfaces, the frequency of aromatic ring participation in anion-quadrupole interactions is comparable to that of positive charge participation in salt bridges, suggesting an underappreciated role for anion-quadrupole interactions at DNA-protein (or membrane-protein) interfaces. Although less frequent than salt bridges in single-chain proteins, we observed highly conserved anion-quadrupole interactions in the structures of remote homologues, and evolutionary covariance-based residue contact score predictions suggest that conserved anion-quadrupole interacting pairs, like salt bridges, contribute to polypeptide folding, stability, and recognition.

SVMQA: support-vector-machine-based protein single-model quality assessment

Motivation

The accurate ranking of predicted structural models and selecting the best model from a given candidate pool remain as open problems in the field of structural bioinformatics. The quality assessment (QA) methods used to address these problems can be grouped into two categories: consensus methods and single-model methods. Consensus methods in general perform better and attain higher correlation between predicted and true quality measures. However, these methods frequently fail to generate proper quality scores for native-like structures which are distinct from the rest of the pool. Conversely, single-model methods do not suffer from this drawback and are better suited for real-life applications where many models from various sources may not be readily available.

Results

In this study, we developed a support-vector-machine-based single-model global quality assessment (SVMQA) method. For a given protein model, the SVMQA method predicts TM-score and GDT_TS score based on a feature vector containing statistical potential energy terms and consistency-based terms between the actual structural features (extracted from the three-dimensional coordinates) and predicted values (from primary sequence). We trained SVMQA using CASP8, CASP9 and CASP10 targets and determined the machine parameters by 10-fold cross-validation. We evaluated the performance of our SVMQA method on various benchmarking datasets. Results show that SVMQA outperformed the existing best single-model QA methods both in ranking provided protein models and in selecting the best model from the pool. According to the CASP12 assessment, SVMQA was the best method in selecting good-quality models from decoys in terms of GDTloss.

Availability and implementation

SVMQA method can be freely downloaded from http://lee.kias.re.kr/SVMQA/SVMQA_eval.tar.gz.

Contact

jlee@kias.re.kr.

Supplementary information

Supplementary data are available at Bioinformatics online.

What makes it difficult to refine protein models further via molecular dynamics simulations?

Protein structure refinement remains a challenging yet important problem as it has the potential to bring already accurate template-based models to near-native resolution. Refinement based on molecular dynamics simulations has been a highly promising approach and the performance of MD-based refinement in the Feig group during CASP12 is described here. During CASP12, sampling was extended well into the microsecond scale, an improved force field was applied, and new protocol variations were tested. Progress over previous rounds of CASP was found to be limited which is analyzed in terms of the quality of the initial models and dependency on the amount of sampling and refinement protocol variations. As current MD-based refinement protocols appear to be reaching a plateau, detailed analysis is presented to provide new insight into the major challenges towards more extensive structure refinement, focusing in particular on sampling with and without restraints.

Grid-based prediction of torsion angle probabilities of protein backbone and its application to discrimination of protein intrinsic disorder regions and selection of model structures

BACKGROUND

Protein structure can be described by backbone torsion angles: rotational angles about the N-Cα bond (φ) and the Cα-C bond (ψ) or the angle between Cαi-1-Cαi-Cαi + 1 (θ) and the rotational angle about the Cαi-Cαi + 1 bond (τ). Thus, their accurate prediction is useful for structure prediction and model refinement. Early methods predicted torsion angles in a few discrete bins whereas most recent methods have focused on prediction of angles in real, continuous values. Real value prediction, however, is unable to provide the information on probabilities of predicted angles.

RESULTS

Here, we propose to predict angles in fine grids of 5° by using deep learning neural networks. We found that this grid-based technique can yield 2-6% higher accuracy in predicting angles in the same 5° bin than existing prediction techniques compared. We further demonstrate the usefulness of predicted probabilities at given angle bins in discrimination of intrinsically disorder regions and in selection of protein models.

CONCLUSIONS

The proposed method may be useful for characterizing protein structure and disorder. The method is available at http://sparks-lab.org/server/SPIDER2/ as a part of SPIDER2 package.

Diverse effects of distance cutoff and residue interval on the performance of distance-dependent atom-pair potential in protein structure prediction

BACKGROUND

As one of the most successful knowledge-based energy functions, the distance-dependent atom-pair potential is widely used in all aspects of protein structure prediction, including conformational search, model refinement, and model assessment. During the last two decades, great efforts have been made to improve the reference state of the potential, while other factors that also strongly affect the performance of the potential have been relatively less investigated.

RESULTS

Based on different distance cutoffs (from 5 to 22 Å) and residue intervals (from 0 to 15) as well as six different reference states, we constructed a series of distance-dependent atom-pair potentials and tested them on several groups of structural decoy sets collected from diverse sources. A comprehensive investigation has been performed to clarify the effects of distance cutoff and residue interval on the potential's performance. Our results provide a new perspective as well as a practical guidance for optimizing distance-dependent statistical potentials.

CONCLUSIONS

The optimal distance cutoff and residue interval are highly related with the reference state that the potential is based on, the measurements of the potential's performance, and the decoy sets that the potential is applied to. The performance of distance-dependent statistical potential can be significantly improved when the best statistical parameters for the specific application environment are adopted.

Template-based and free modeling of I-TASSER and QUARK pipelines using predicted contact maps in CASP12

We develop two complementary pipelines, "Zhang-Server" and "QUARK", based on I-TASSER and QUARK pipelines for template-based modeling (TBM) and free modeling (FM), and test them in the CASP12 experiment. The combination of I-TASSER and QUARK successfully folds three medium-size FM targets that have more than 150 residues, even though the interplay between the two pipelines still awaits further optimization. Newly developed sequence-based contact prediction by NeBcon plays a critical role to enhance the quality of models, particularly for FM targets, by the new pipelines. The inclusion of NeBcon predicted contacts as restraints in the QUARK simulations results in an average TM-score of 0.41 for the best in top five predicted models, which is 37% higher than that by the QUARK simulations without contacts. In particular, there are seven targets that are converted from non-foldable to foldable (TM-score >0.5) due to the use of contact restraints in the simulations. Another additional feature in the current pipelines is the local structure quality prediction by ResQ, which provides a robust residue-level modeling error estimation. Despite the success, significant challenges still remain in ab initio modeling of multi-domain proteins and folding of β-proteins with complicated topologies bound by long-range strand-strand interactions. Improvements on domain boundary and long-range contact prediction, as well as optimal use of the predicted contacts and multiple threading alignments, are critical to address these issues seen in the CASP12 experiment.

OPUS-CSF: A C-atom-based scoring function for ranking protein structural models

We report a C‐atom‐based scoring function, named OPUS‐CSF, for ranking protein structural models. Rather than using traditional Boltzmann formula, we built a scoring function (CSF score) based on the native distributions (derived from the entire PDB) of coordinate components of mainchain C (carbonyl) atoms on selected residues of peptide segments of 5, 7, 9, and 11 residues in length. In testing OPUS‐CSF on decoy recognition, it maximally recognized 257 native structures out of 278 targets in 11 commonly used decoy sets, significantly outperforming other popular all‐atom empirical potentials. The average correlation coefficient with TM‐score was also comparable with those of other potentials. OPUS‐CSF is a highly coarse‐grained scoring function, which only requires input of partial mainchain information, and very fast. Thus, it is suitable for applications at early stage of structural building.

QAcon: single model quality assessment using protein structural and contact information with machine learning techniques

Motivation

Protein model quality assessment (QA) plays a very important role in protein structure prediction. It can be divided into two groups of methods: single model and consensus QA method. The consensus QA methods may fail when there is a large portion of low quality models in the model pool.

Results

In this paper, we develop a novel single-model quality assessment method QAcon utilizing structural features, physicochemical properties, and residue contact predictions. We apply residue-residue contact information predicted by two protein contact prediction methods PSICOV and DNcon to generate a new score as feature for quality assessment. This novel feature and other 11 features are used as input to train a two-layer neural network on CASP9 datasets to predict the quality of a single protein model. We blindly benchmarked our method QAcon on CASP11 dataset as the MULTICOM-CLUSTER server. Based on the evaluation, our method is ranked as one of the top single model QA methods. The good performance of the features based on contact prediction illustrates the value of using contact information in protein quality assessment.

Availability and Implementation

The web server and the source code of QAcon are freely available at: http://cactus.rnet.missouri.edu/QAcon.

Contact

chengji@missouri.edu.

Supplementary information

Supplementary data are available at Bioinformatics online.

Protein structure model refinement in CASP12 using short and long molecular dynamics simulations in implicit solvent

Protein structure prediction has matured over years, particularly those which use structure templates for building a model. It can build a model with correct overall conformation in cases where appropriate templates are available. Models with the correct topology can be practically useful for limited purposes that need residue-level accuracy, but further improvement of the models can allow the models to be used in tasks that need detailed structures, such as molecular replacement in X-ray crystallography or structure-based drug screening. Thus, model refinement is an important final step in protein structure prediction to bridge predictions to real-life applications. Model refinement is one of the categories in recent rounds of critical assessment of techniques in protein structure prediction (CASP) and has recently been drawing more attention due to its realized importance. Here we report our group's performance in the refinement category in CASP12. Our method is based on inexpensive short molecular dynamics (MD) simulations in implicit solvent. Our performance in CASP12 was among the top, which was consistent with the previous round, CASP11. Our method with short MD runs achieved comparable performance with other methods that used longer simulations. Detailed analyses found that improvements typically occurred in entire regions of a structure rather than only in flexible loop regions. The remaining challenge in the structure refinement includes large conformational refinement which involves substantial motions of secondary structure elements or domains.

OPUS-DOSP: A Distance- and Orientation-Dependent All-Atom Potential Derived from Side-Chain Packing

We report a new distance- and orientation-dependent, all-atom statistical potential derived from side-chain packing, named OPUS-DOSP, for protein structure modeling. The framework of OPUS-DOSP is based on OPUS-PSP, previously developed by us [JMB (2008), 376, 288-301], with refinement and new features. In particular, distance or orientation contribution is considered depending on the range of contact distance. A new auxiliary function in energy function is also introduced, in addition to the traditional Boltzmann term, in order to adjust the contributions of extreme cases. OPUS-DOSP was tested on 11 decoy sets commonly used for statistical potential benchmarking. Among 278 native structures, 239 and 249 native structures were recognized by OPUS-DOSP without and with the auxiliary function, respectively. The results show that OPUS-DOSP has an increased decoy recognition capability comparing with those of other relevant potentials to date.

Sequence statistics of tertiary structural motifs reflect protein stability

The Protein Data Bank (PDB) has been a key resource for learning general rules of sequence-structure relationships in proteins. Quantitative insights have been gained by defining geometric descriptors of structure (e.g., distances, dihedral angles, solvent exposure, etc.) and observing their distributions and sequence preferences. Here we argue that as the PDB continues to grow, it may become unnecessary to reduce structure into a set of elementary descriptors. Instead, it could be possible to deduce quantitative sequence-structure relationships in the context of precisely-defined complex structural motifs by mining the PDB for closely matching backbone geometries. To validate this idea, we turned to the the task of predicting changes in protein stability upon amino-acid substitution—a difficult problem of broad significance. We defined non-contiguous tertiary motifs (TERMs) around a protein site of interest and extracted sequence preferences from ensembles of closely-matching substructures in the PDB to predict mutational stability changes at the site, ΔΔG_m. We demonstrate that these ensemble statistics predict ΔΔG_m on par with state-of-the-art statistical and machine-learning methods on large thermodynamic datasets, and outperform these, along with a leading structure-based modeling approach, when tested in the context of unbiased diverse mutations. Further, we show that the performance of the TERM-based method is directly related to the amount of available relevant structural data, automatically improving with the growing PDB. This enables a means of estimating prediction accuracy. Our results clearly demonstrate that: 1) statistics of non-contiguous structural motifs in the PDB encode fundamental sequence-structure relationships related to protein thermodynamic stability, and 2) the PDB is now large enough that such statistics are already useful in practice, with their accuracy expected to continue increasing as the database grows. These observations suggest new ways of using structural data towards addressing problems of computational structural biology.

MQAPRank: improved global protein model quality assessment by learning-to-rank

BACKGROUND

Protein structure prediction has achieved a lot of progress during the last few decades and a greater number of models for a certain sequence can be predicted. Consequently, assessing the qualities of predicted protein models in perspective is one of the key components of successful protein structure prediction. Over the past years, a number of methods have been developed to address this issue, which could be roughly divided into three categories: single methods, quasi-single methods and clustering (or consensus) methods. Although these methods achieve much success at different levels, accurate protein model quality assessment is still an open problem.

RESULTS

Here, we present the MQAPRank, a global protein model quality assessment program based on learning-to-rank. The MQAPRank first sorts the decoy models by using single method based on learning-to-rank algorithm to indicate their relative qualities for the target protein. And then it takes the first five models as references to predict the qualities of other models by using average GDT_TS scores between reference models and other models. Benchmarked on CASP11 and 3DRobot datasets, the MQAPRank achieved better performances than other leading protein model quality assessment methods. Recently, the MQAPRank participated in the CASP12 under the group name FDUBio and achieved the state-of-the-art performances.

CONCLUSIONS

The MQAPRank provides a convenient and powerful tool for protein model quality assessment with the state-of-the-art performances, it is useful for protein structure prediction and model quality assessment usages.

Structure-based prediction of Wnt binding affinities for Frizzled-type cysteine-rich domains

Wnt signaling pathways are of significant interest in development and oncogenesis. The first step in these pathways typically involves the binding of a Wnt protein to the cysteine-rich domain (CRD) of a Frizzled receptor. Wnt-Frizzled interactions can be antagonized by secreted Frizzled-related proteins (SFRPs), which also contain a Frizzled-like CRD. The large number of Wnts, Frizzleds, and SFRPs, as well as the hydrophobic nature of Wnt, poses challenges to laboratory-based investigations of interactions involving Wnt. Here, utilizing structural knowledge of a representative Wnt-Frizzled CRD interaction, as well as experimentally determined binding affinities for a selection of Wnt-Frizzled CRD interactions, we generated homology models of Wnt-Frizzled CRD interactions and developed a quantitative structure-activity relationship for predicting their binding affinities. The derived model incorporates a small selection of terms derived from scoring functions used in protein-protein docking, as well as an energetic term considering the contribution made by the lipid of Wnt to the Wnt-Frizzled binding affinity. Validation with an external test set suggests that the model can accurately predict binding affinity for 75% of cases and that the error associated with the predictions is comparable with the experimental error. The model was applied to predict the binding affinities of the full range of mouse and human Wnt-Frizzled and Wnt-SFRP interactions, indicating trends in Wnt binding affinity for Frizzled and SFRP CRDs. The comprehensive predictions made in this study provide the basis for laboratory-based studies of previously unexplored Wnt-Frizzled and Wnt-SFRP interactions, which, in turn, may reveal further Wnt signaling pathways.

Discrimination of Native-like States of Membrane Proteins with Implicit Membrane-based Scoring Functions

A scoring protocol based on implicit membrane-based scoring functions and a new protocol for optimizing the positioning of proteins inside the membrane was evaluated for its capacity to discriminate native-like states from misfolded decoys. A decoy set previously established by the Baker lab (Proteins: Struct., Funct., Genet. 2006, 62, 1010-1025) was used along with a second set that was generated to cover higher resolution models. The Implicit Membrane Model 1 (IMM1), IMM1 model with CHARMM 36 parameters (IMM1-p36), generalized Born with simple switching (GBSW), and heterogeneous dielectric generalized Born versions 2 (HDGBv2) and 3 (HDGBv3) were tested along with the new HDGB van der Waals (HDGBvdW) model that adds implicit van der Waals contributions to the solvation free energy. For comparison, scores were also calculated with the distance-scaled finite ideal-gas reference (DFIRE) scoring function. Z-scores for native state discrimination, energy vs root-mean-square deviation (RMSD) correlations, and the ability to select the most native-like structures as top-scoring decoys were evaluated to assess the performance of the scoring functions. Ranking of the decoys in the Baker set that were relatively far from the native state was challenging and dominated largely by packing interactions that were captured best by DFIRE with less benefit of the implicit membrane-based models. Accounting for the membrane environment was much more important in the second decoy set where especially the HDGB-based scoring functions performed very well in ranking decoys and providing significant correlations between scores and RMSD, which shows promise for improving membrane protein structure prediction and refinement applications. The new membrane structure scoring protocol was implemented in the MEMScore web server ( http://feiglab.org/memscore ).